1. Limit Evaluation Set A (View Solutions 1a - 1i)
Problem 1(a)
\(\displaystyle \lim_{x \to 1 } \dfrac{x^2-1}{x-1}\)
Problem 1(b)
\(\displaystyle \lim_{x \to -1 } \dfrac{x^2-1}{x+1}\)
Problem 1(c)
\(\displaystyle \lim_{x \to 2 } \dfrac{x^2-4}{x-2} \)
Problem 1(d)
\(\displaystyle \lim_{x \to 1 } \dfrac{x^2-3x+2}{2x-2}\)
Problem 1(e)
\(\displaystyle \lim_{x \to -2} \dfrac{x^2+5x+6}{x^2+2x}\)
Problem 1(f)
\(\displaystyle \lim_{x \to 3 } \dfrac{x^2-5x+6}{x^2-9}\)
Problem 1(g)
\(\displaystyle \lim_{x \to \infty} \dfrac{2x^3-6x^2+5}{6x^3-3x+5}\)
Problem 1(h)
\(\displaystyle \lim_{x \to \infty} \dfrac{2x^5-6x^2+5}{3x^4-3x+5}\)
Problem 1(i)
\(\displaystyle \lim_{x \to- \infty} \dfrac{5x^4-6x+15}{2x^5-x^2+7}\)
2. Limit Evaluation Set B (View Solutions 2a - 2e)
Problem 2(a)
\(\displaystyle \lim_{x \to \frac{1}{2}} \left[ \cos (\pi x) - e^{x-\frac{1}{2}} \right]\)
Problem 2(b)
\(\displaystyle \lim_{x \to -1}\frac{x^2-x-2}{7x+7}\)
Problem 2(c)
\(\displaystyle \lim_{h \to 0}\frac{\sqrt{16+h}-4}{h}\)
Problem 2(d)
\(\displaystyle \lim_{x \to 0}\dfrac{\frac{1}{x+4}-\frac{1}{4}}{x}\)
Problem 2(e)
\(\displaystyle \lim_{x \to \infty} \dfrac{3x^5+5x+2}{2x^5-2x^3+1}\)